1. Field of the Invention
The present invention relates to an electronic beam lithography and, more particularly, to a method and device for proximity effect correction of electronic beam exposure.
2. Description of the Related Art
Electron beam lithography is a technique used in forming a feature pattern on a material layer of a substrate. This entails the process of coating a material layer of a wafer with photoresist; writing a desired pattern onto the material layer by projecting an electron beam (referred to in the art as an xe2x80x9cexposurexe2x80x9d); developing the electron beam resist; and etching the resist material layer and leaving the desired pattern on the wafer. Electron beam lithography is commonly used to form a predetermined material layer pattern, forming an integrated circuit on the substrate. Similarly, electron beam lithography is also used to fabricate a photomask.
During electron beam exposure, proximity effect due to scattered electrons in a resist layer and a substrate considerably affects the accuracy of a pattern line width. Thus, the proximity effect is generally corrected by a compensation method. To estimate a value of the proximity effect, energy distribution accumulated in the resist layer can be represented as:                               f          ⁡                      (            r            )                          =                              1                          π              ⁡                              (                                  1                  +                  η                                )                                              ⁡                      [                                                            1                                      α                    2                                                  ⁢                                  exp                  ⁡                                      (                                                                  -                                                  r                          2                                                                                            α                        2                                                              )                                                              +                                                η                                      β                    2                                                  ⁢                                  exp                  ⁡                                      (                                                                  -                                                  r                          2                                                                                            β                        2                                                              )                                                                        ]                                              [                  Equation          ⁢                      xe2x80x83                    ⁢          1                ]            
wherein r is a distance between an electron incident point and an intensity calculation point, xcex1 is a parameter representing a forward scattering region, xcex2 is a parameter representing a backward scattering region, and xcex7 is a backward scattering coefficient, which is a ratio of an accumulated energy by backward scattering electrons and an accumulated energy by forward scattering electrons.
The backward scattering coefficient xcex7 is a constant which is dependent on a material such as a substrate and a resist layer. Therefore, the backward scattering coefficient xcex7 is a function of atomic weight, density, and thickness of an underlying material to be etched after exposure. If various pattern shapes having a same design critical dimension(CD) are formed, CD distribution can be varied with respective pattern densities. Therefore, if the proximity effect correction depends on a constant backward scattering coefficient xcex7, the design of a highly integrated semiconductor device having a uniform pattern dimension can be difficult.
Furthermore, the electron beam does not expose only the desired portion of the resist layer, as the electron beam is reflected on a surface of an opaque film (which is formed between the resist layer and the substrate) or scattered by collisions with atoms of a resist material in the resist layer. Also, the electron beam is reflected in the electron beam resist and at the lower plane of an objective lens of an electron beam writer and, as a sequence, the electron beam exposes an undesired portion of the resist layer. The pattern dimension variation caused by the former additional exposure is referred to as a proximity effect. The pattern dimension variation caused by the latter additional exposure is referred to as a re-scattering effect or a fogging effect of the electron beam, and the pattern dimension variation caused by a pattern density is referred to as a loading effect.
Although numerous prior art methods for reducing the fogging effect and the loading effect have been proposed, there is a limitation to finely correct the pattern dimension variation for manufacturing highly integrated circuits. This is largely due to the fogging effect and the loading effect being correlated after assuming the backward scattering coefficient xcex7 as a constant.
Therefore, it is highly desirable to provide a method and recordable medium for controlling an electron beam for compensation of variation of line width by the fogging effect and the loading effect.
An electron beam exposure method is provided, which includes the steps of: dividing an exposure region into a plurality of grating regions; obtaining a pattern density for one of the plurality of grating regions; determining a backward scattering coefficient in accordance with the pattern density for the one of the plurality of grating regions; calculating an exposure dose amount from the backward scattering coefficient; and exposing the one of the plurality of grating regions with the calculated exposure dose amount.
According to an embodiment of the present invention, the backward scattering coefficient is provided with a variable function proportional to the pattern density. The backward scattering coefficient is provided with a variable value depending on the pattern density and location of the one of the plurality of grating regions. The plurality of grating regions include a first grating region having a patterning region having a first backward scattering coefficient and a second grating region having a surrounding region not including the patterning region and a second backward scattering coefficient, wherein the second backward scattering coefficient is higher than the first backward scattering coefficient.
An electron beam exposure method is also provided, which includes the steps of: dividing an exposure region into a plurality of grating regions; obtaining respective pattern densities for the plurality of grating regions; generating a pattern map with locations of the exposure region in accordance with the pattern densities in the respective plurality of grating regions; determining backward scattering coefficients for the plurality of grating regions in accordance with the respective pattern densities and the locations of the exposure region; generating a backward scattering coefficient map with the locations of the exposure region in accordance with the backward scattering coefficients; calculating an exposure dose amount for the plurality of grating regions in accordance with the backward scattering coefficients obtained from the backward scattering coefficient map; and exposing the plurality of grating regions with the calculated exposure dose amount.
According to an embodiment of the present invention, the backward scattering coefficients are provided with a variable function proportional to the pattern densities. The backward scattering coefficients are provided with variable values depending on the pattern densities and the locations of the grating regions. The plurality of grating regions include a first grating region having a patterning region having a first backward scattering coefficient and a second grating region having a surrounding region not including the pattern region and a second backward scattering coefficient, wherein the second backward scattering coefficient is higher than the first backward scattering coefficient of the first grating region. The step of the calculating the exposure dose amount includes the following equation:       D    ⁢          (              d        r            )        =                    1        +                  2          ⁢          η                            1        +                  2          ⁢                      d            r                    ⁢          η                      ·          D      ⁢              (        1        )            
wherein D(dr) is the exposure dose amount, xcex7 is the backward scattering coefficient, dr is a pattern density at a predetermined location, 0xe2x89xa6drxe2x89xa61, D(1) is an exposure dose amount having the pattern density of 100%. The step of the calculating the exposure dose amount comprises the steps of: calculating an exposure dose amount by following equation:       D    ⁢          (              d        r            )        =                    1        +                  2          ⁢          η                            1        +                  2          ⁢                      d            r                    ⁢          η                      ·          D      ⁢              (        1        )            
wherein D(dr) is the exposure dose amount, xcex7 is the backward scattering coefficient, dr is a pattern density at a predetermined location, 0xe2x89xa6drxe2x89xa61, D(1) is an exposure dose amount having the pattern density of 100%; and obtaining a corrected dose amount by subtracting an increased dose amount xcex94D(dr) at the predetermined location from the exposure dose amount D(dr). The increased dose amount xcex94D(dr) is obtained by a variation of the backward scattering coefficient at the predetermined location of the grating region, when the backward scattering coefficient is increased from xcex71 to xcex72, the increased dose amount xcex94D(dr) is obtained by following equation:       Δ    ⁢          xe2x80x83        ⁢          D      ⁢              (                  d          r                )              =                    2        ⁢                  (                      1            -                          d              r                                )                ⁢                  (                                    η              2                        -                          η              1                                )                                      (                      1            +                          2              ⁢                              d                r                            ⁢                              η                1                                              )                ⁢                  (                      1            +                          2              ⁢                              d                r                            ⁢                              η                2                                              )                      ·          D      ⁢              (        1        )            
wherein dr is a pattern density at the predetermined location, 0xe2x89xa6drxe2x89xa61, D(1) is an exposure dose amount having the pattern density of 100%.
A recording medium having stored modules with instructions executable by a computer to perform a corrected electron beam exposure is also provided, the recording medium includes: a first program module for obtaining a pattern density in one grating region produced by dividing an exposure surface into a plurality of grating regions; a second program module for obtaining a backward scattering coefficient xcex7 at the one grating region in accordance with the pattern density; and a third program module for obtaining an exposure dose amount from the backward scattering coefficient.
According to an embodiment of the present invention, the second program module includes a sub-program module for deciding the backward scattering coefficient xcex7 in accordance with a predetermined function in which the backward scattering coefficient xcex7 is proportional to the pattern density. The second program module includes a sub-program module for deciding the backward scattering coefficient xcex7, the backward scattering coefficient xcex7 is variable in accordance with the pattern density and a location of the grating region. The plurality of grating regions includes a first grating region having a patterning region having a first backward scattering coefficient and a second grating region having a surrounding region not including the patterning region having a second backward scattering coefficient, the second program module includes a sub-program module in which the second backward scattering coefficient is higher than the first backward scattering coefficient.
A recording medium having stored programs executable by a computer for performing a corrected electron beam exposure is also provided, the recording medium includes: a first program module for obtaining pattern densities of a plurality of grating regions divided by an exposure surface; a second program module for obtaining a pattern density map with locations of the plurality of grating regions in accordance with the pattern densities; a third program module for obtaining backward scattering coefficients at the plurality of grating regions in accordance with the pattern density and the location of exposure region; a fourth program module for generating a backward scattering coefficient map in accordance with the backward scattering coefficients; and a fifth program module for obtaining a corrected expose dose amount at one of the plurality of grating regions in accordance with the backward scattering coefficient.
According to an embodiment of the present invention, the third program module includes a sub-program module in which the backward scattering coefficient is provided with a variable function proportional to the pattern density. The third program module includes a sub-program module in which the backward scattering coefficient is provided with a variable value depending on the pattern density and the location of the grating region. The plurality of grating regions includes a first grating region having a patterning region having a first backward scattering coefficient and a second grating region having a surrounding region not including the patterning region and a second backward scattering coefficient, wherein the second program module includes a sub-program module in which the first backward scattering coefficient is higher than the second backward scattering coefficient. The fifth program module includes a sub-program module for calculating an exposure dose amount by following equation:       D    ⁢          (              d        r            )        =                    1        +                  2          ⁢          η                            1        +                  2          ⁢                      d            r                    ⁢          η                      ·          D      ⁢              (        1        )            
wherein D(dr) is the exposure dose amount, xcex7 is the backward scattering coefficient, dr is a pattern density at a predetermined location, 0xe2x89xa6dr less than 1, D(1) is an exposure dose amount having the pattern density of 100%. The fifth program module includes: a first sub-program module for calculating an exposure dose amount by following equation:       D    ⁢          (              d        r            )        =                    1        +                  2          ⁢          η                            1        +                  2          ⁢                      d            r                    ⁢          η                      ·          D      ⁢              (        1        )            
wherein D(dr) is the exposure dose amount, xcex7 is the backward scattering coefficient, dr is a pattern density at a predetermined location, 0xe2x89xa6drxe2x89xa61, D(1) is an exposure dose amount having the pattern density of 100%; and a second sub-program module for obtaining a corrected dose amount by subtracting an increased dose amount xcex94D(dr) at a predetermined location from the exposure dose amount D(dr). The increased dose amount xcex94D(dr) is obtained by a variation of the backward scattering coefficient at a predetermined location of the grating region, when the backward scattering coefficient is increased from xcex71 to xcex72, the increased dose amount xcex94D(dr) is obtained by following equation:       Δ    ⁢          xe2x80x83        ⁢          D      ⁢              (                  d          r                )              =                    2        ⁢                  (                      1            -                          d              r                                )                ⁢                  (                                    η              2                        -                          η              1                                )                                      (                      1            +                          2              ⁢                              d                r                            ⁢                              η                1                                              )                ⁢                  (                      1            +                          2              ⁢                              d                r                            ⁢                              η                2                                              )                      ·          D      ⁢              (        1        )            
wherein dr is a pattern density at the predetermined location, 0xe2x89xa6dr less than 1, D(1) is an exposure dose amount having the pattern density of 100%.